Evaluation of Orthometric and Related Height Systems Using a Simulated Mountain Gravity Field

Abstract

With the widespread computation of gravimetric geoid and quasi-geoid models for GPS height transformation, there is renewed interest in defining vertical datums using height systems that are fully compatible with GPS-derived heights. Although orthometric heights are commonly used for such purposes, computation of their true value from spirit leveling observations requires an exact knowledge of gravity along the (curved) plumbline above the geoid. Without direct gravity observations, several hypotheses must be made, and as such, numerous variants (approximations) of the true orthometric height have been derived. This paper evaluates six height systems using a simulated (exact) gravity field from a well-defined prismoidal mountain mass for which the gravity field and plumblines are unambiguously defined. From this, the simulated (true) orthometric heights are computed and compared to various approximate orthometric heights. Geometric (ellipsoidal), normal, and dynamic heights are also evaluated. Comparisons of the height systems are made regarding their utility, accuracy, and compatibility with gravimetric geoid and quasi-geoid models.